Blundell Thermal Physics · Problem 26.3

Real gases

Physics — Statistical Mechanics · dieterici-equation-reduced-units

Problem

Show that the Dieterici equation of state, p(V−b)=RTe−a/RTV,p(V - b) = RT\mathrm{e}^{-a/RTV}, can be written in reduced units as P~(2V~−1)=T~exp⁡[2(1−1T~V~)],\tilde{P}(2\tilde{V} - 1) = \tilde{T} \exp\left[2\left(1 - \frac{1}{\tilde{T}\tilde{V}}\right)\right], where P~=P/Pc\tilde{P} = P/P_c, T~=T/Tc\tilde{T} = T/T_c, V~=V/Vc\tilde{V} = V/V_c, and (Pc,Tc,Vc)(P_c, T_c, V_c) is the critical point.

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